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Simplifying 3(x + 1) + -2(x + 3) + 2(x + -4) + 3(x + -2) = 0 Reorder the terms: 3(1 + x) + -2(x + 3) + 2(x + -4) + 3(x + -2) = 0 (1 * 3 + x * 3) + -2(x + 3) + 2(x + -4) + 3(x + -2) = 0 (3 + 3x) + -2(x + 3) + 2(x + -4) + 3(x + -2) = 0 Reorder the terms: 3 + 3x + -2(3 + x) + 2(x + -4) + 3(x + -2) = 0 3 + 3x + (3 * -2 + x * -2) + 2(x + -4) + 3(x + -2) = 0 3 + 3x + (-6 + -2x) + 2(x + -4) + 3(x + -2) = 0 Reorder the terms: 3 + 3x + -6 + -2x + 2(-4 + x) + 3(x + -2) = 0 3 + 3x + -6 + -2x + (-4 * 2 + x * 2) + 3(x + -2) = 0 3 + 3x + -6 + -2x + (-8 + 2x) + 3(x + -2) = 0 Reorder the terms: 3 + 3x + -6 + -2x + -8 + 2x + 3(-2 + x) = 0 3 + 3x + -6 + -2x + -8 + 2x + (-2 * 3 + x * 3) = 0 3 + 3x + -6 + -2x + -8 + 2x + (-6 + 3x) = 0 Reorder the terms: 3 + -6 + -8 + -6 + 3x + -2x + 2x + 3x = 0 Combine like terms: 3 + -6 = -3 -3 + -8 + -6 + 3x + -2x + 2x + 3x = 0 Combine like terms: -3 + -8 = -11 -11 + -6 + 3x + -2x + 2x + 3x = 0 Combine like terms: -11 + -6 = -17 -17 + 3x + -2x + 2x + 3x = 0 Combine like terms: 3x + -2x = 1x -17 + 1x + 2x + 3x = 0 Combine like terms: 1x + 2x = 3x -17 + 3x + 3x = 0 Combine like terms: 3x + 3x = 6x -17 + 6x = 0 Solving -17 + 6x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + 6x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 6x = 0 + 17 6x = 0 + 17 Combine like terms: 0 + 17 = 17 6x = 17 Divide each side by '6'. x = 2.833333333 Simplifying x = 2.833333333
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